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The finite element method for non-linear problems
Applications of Mathematics, Tome 15 (1970) no. 3, pp. 177-189
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The paper deals with the method of finite elements which is substantially the generalized Ritz method using a special choice of basis functions. The method has been applied by some authors to non-linear ordinary differential equations as well as to linear partial differential equations. In the present paper, the method is used for solving non-linear operator equations. The left hand operator of the equation is potential and fulfils some boundedness conditions. These assumptions imply the unique existence of both exact and approximate solution of the equation as well as an estimate of its error. The results are used for solving the general quasilinear equation.
The paper deals with the method of finite elements which is substantially the generalized Ritz method using a special choice of basis functions. The method has been applied by some authors to non-linear ordinary differential equations as well as to linear partial differential equations. In the present paper, the method is used for solving non-linear operator equations. The left hand operator of the equation is potential and fulfils some boundedness conditions. These assumptions imply the unique existence of both exact and approximate solution of the equation as well as an estimate of its error. The results are used for solving the general quasilinear equation.
DOI : 10.21136/AM.1970.103284
Classification : 65J05, 65J15 
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Melkes, František. The finite element method for non-linear problems. Applications of Mathematics, Tome 15 (1970) no. 3, pp. 177-189. doi: 10.21136/AM.1970.103284

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